PDE constrained optimization for optical tomograph
2016-08-23
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We report the implementation of an augmented Lagrangian method for solving the inverse problem of diffusion optical tomography (DOT). The forward model of light propagation is the radiative transfer equation (RTE). The inverse problem is transformed into an equality constraint with the RTE minimization problem, which is regarded as a pair set of "optical properties - quaternion". This method allows the recently developed PDE constrained optimization, which shows great hope in many applications and the introduction of techniques that can be formulated as infinite dimensional optimization problems. Compared with the traditional unconstrained optimization method for optical tomography, one of them solves several forward and adjoint problems, and each optimization iteration, the method proposed in this work solves both forward and backward problems. In our initial study, we found that using synthetic data, the image reconstruction time can typically pass 10 to 30 times, which depends on the combination of noise level, regularization parameters, mesh size, initial guess, optical performance and geometry of the system.
matlab
PDE
优化
扫描
问题
约束
断层
光学
反向
正向
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